Connected and Disconnected Contractions in Pion-Pion Scattering

Abstract

We show that the interplay of chiral effective field theory and lattice QCD can be used in the evaluation of so-called disconnected diagrams, which appear in the study of the isoscalar and isovector channels of pion-pion scattering and have long been a major challenge for the lattice community. By means of partially-quenched chiral perturbation theory, we distinguish and analyze the effects from different types of contraction diagrams to the pion-pion scattering amplitude, including its scattering lengths and the energy-dependence of its imaginary part. Our results may be used to test the current degree of accuracy of lattice calculation in the handling of disconnected diagrams, as well as to set criteria for the future improvement of relevant lattice computational techniques that may play a critical role in the study of other interesting QCD matrix elements.

18 pages, 3 figures, 3 tables

References in corpus (14)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Mesonic low-energy constants
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• Timelike pion form factor in lattice QCD
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• The phase-shift of isospin-2 pi-pi scattering from lattice QCD
• Quark disconnected diagrams in chiral perturbation theory
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Isospin-0 $\pi \pi$ s-wave scattering length from twisted mass lattice QCD
• Applications of Chiral Perturbation theory to lattice QCD

Cited by in corpus (11)

• FLAG Review 2019
• FLAG Review 2021
• Coarse graining $\pi \pi$ scattering
• Effective Field Theory in The Study of Long Range Nuclear Parity Violation on Lattice
• Applicability of the two-particle quantization condition to partially-quenched theories
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation
• Contraction Diagram Analysis in Pion-Kaon Scattering
• Constraints on Disconnected Contributions in $\pi \pi$ Scattering
• Another walk through the world of chiral dynamics
• Extracting the low-energy constant $L_0^r$ at three flavors from pion-kaon scattering